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Laws of the Iterated Logarithm for the Empirical Characteristic Function
Michael T. Lacey
The Annals of Probability
Vol. 17, No. 1 (Jan., 1989), pp. 292-300
Published by: Institute of Mathematical Statistics
Stable URL: http://www.jstor.org/stable/2244211
Page Count: 9
You can always find the topics here!Topics: Eigenfunctions, Random variables, Logarithms, Banach space, Distribution functions, Central limit theorem, Convexity, Probabilities, Log integral function
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Let X be a real-valued random variable with distribution function F(x) and characteristic function c(t). Let Fn(x) be the nth empirical distribution function associated with X and let cn(t) be the characteristic function Fn(x). Necessary and sufficient conditions in terms of c(t) are obtained for cn(t) - c(t) to obey bounded and compact laws of the iterated logarithm in the Banach space of continuous complex-valued functions on [ -1, 1 ].
The Annals of Probability © 1989 Institute of Mathematical Statistics